Complexity of warped conformal field theory

Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro�Kac�Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS<inf>3</inf> spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT<inf>2</inf>�s using circuit complexity as a tool. First we compute the holographic volume complexity (CV) which displays a linear UV divergence structure, more akin to that of a local CFT<inf>2</inf> and has a very complicated dependence on the Virasoro central charge c and the U(1) Kac�Moody level parameter k. Next we consider circuit complexity based on Virasoro�Kac�Moody symmetry gates where the complexity functional is the geometric (group) action on coadjoint orbits of the Virasoro�Kac�Moody group. We consider a special solution to extremization equations for which complexity scales linearly with �time�. In the semiclassical limit (large c,�k, while c/k remains finite and small) both the holographic volume complexity and circuit complexity scales with k. � 2023 Elsevier B.V., All rights reserved.